The length of the longer diagonal of the parallelogram constructed on \( 5 \vec{a}+2 \vec{b} \) ...

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The length of the longer diagonal of the parallelogram constructed on \( 5 \vec{a}+2 \vec{b} \) and \( \vec{a}-3 \vec{b} \) if it is given that \( |\vec{a}|=2 \sqrt{2},|\vec{b}|=3 \) and angle between \( \vec{a} \) and \( \vec{b} \) is \( \pi / 4 \)
(A) 15
(B) \( \sqrt{113} \)
(C) \( \sqrt{593} \)
(D) \( \sqrt{369} \)
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